I'm trying to model the flow around a wing with the kw SST turbulence model, but the problem is that momentum equation residuals stall at a value too high no matter which timestep I choose. It looks like the code is trying to solve some kind of transient effect like a wake or free shear layer and this effect isn't captured by the turbulence model although the timestep is increased.

Try: Using a larger physical timestep, then local timescale factor. If that still does not work then run the simulation as a true transient simulation using adaptive timestepping.

I have had some good results lately using the true transient approach for airfoil simulations which refused to converge steady state. The simulations take quite a bit longer but at least I get a converged result.

It seems the case converges running it as a transient simulation, but are these results comparable to steady state RANS model results? what if variables evolve with time? how can these fluctuations be included by the Reynolds averaging?

If the transient model does not reach a steady state then a steady state solution is not applicable so no comparison can be made. If you mean you are expecting the turbulence model to average out the fluctuations leaving a steady state solution - well, actually achieving that is a complicated question requiring a detailed knowledge of turbulence and its modelling. I recommend you have a look at turbulence text books such as "Turbulence Modelling for CFD" by Wilcox.

If the instability is small you may be able to achieve a steady state solution by either a coarser grid, using another spatial differencing scheme or the first order time differencing scheme if a transient simulation.

You also have to consider whether the fluctuations are significant. If the fluctuations do not affect parameters of importance (eg lift or drag) then the fluctuations do not matter. In this case all the fluctuations do is make achieving convergence more difficult.